Political independence, actual and perceived, is as vital to the Federal Reserve as it is to the federal judiciary. Neither institution could function effectively if people thought its actions were no more predictable than the next election result.

Yet there is a fine line between being independent and being unaccountable. A democracy can no more delegate its entire economic policy to an unelected central banker — no matter how brilliant he is — than it could turn over all other policies to nine lawyers in robes — no matter how brilliant they are.

Like that of the judiciary, the Fed’s independence depends on mutual restraint: Just as judges should stick to interpreting the law and not making policy, the Fed should stick to what it does best: setting interest rates according to objective economic analysis. Meanwhile, Congress should avoid publicly second-guessing those technical judgments.

Obviously, these are ideals, from which reality regularly deviates. But even by more realistic standards of Washington behavior, today’s letter from Republican leaders in Congress to Ben S. Bernanke, urging the Fed’s board to “resist further extraordinary intervention in the U.S. economy,” crossed the line. Sadly, it was also inevitable — the foreseeable result of a flawed legal mandate that leaves the Fed unnecessarily exposed to politics.

It’s a free country, and everyone has a right to express his view on Fed policy. Members of Congress, from both parties and all points on the ideological spectrum, bark at the Fed all the time.

But when the speaker of the House and the minority leader of the Senate, and their deputies, all members of a party whose presidential candidates are going around the country criticizing the Fed chairman, join to tell the Fed that “the American people have reason to be skeptical of the Federal Reserve vastly increasing its role in the economy if measurable outcomes cannot be demonstrated” — that’s provocative.

Intentionally or not, it conveys an implicit threat of legislative action if the Fed doesn’t change course.

A message like that, delivered privately, might be okay — barely. But this letter was released to the public in the middle of the Fed’s policy meeting. By alluding to public dissents of several Fed board members, and asking Bernanke to distribute the letter to them, the Republican leaders also seemed to foment internal Fed divisions.

Troubling as it may be, this sort of political pressure is inevitable when an unelected central bank commits immense quantities of national wealth to unconventional policies.

The Fed has acted with good intentions, and, at times, courage. Initially, at least, it got good results: without Fed intervention in 2008, it’s likely that the U.S. would have gone into a deflationary spiral and a 1930s-style Depression.

Nevertheless, the Republicans have a point. It would be a lot easier to defend the Fed’s independence if the clear consensus of expert opinion favored its actions. But there is no such consensus.

When the Supreme Court parses a statute and determines, based on applicable precedent, that this party has the right to sue that party, other people may disagree. But they have to concede that the court was deciding a legal question uniquely within its expertise and its authority.

When the court loosely construes broad constitutional language to guarantee, say, a right to abortion, or to strike down long-standing campaign-finance doctrine, it ventures into the political thicket — and it’s going to come under political attack.

Right now, the Fed is a bit like the Supreme Court in Roe v. Wade. It’s pursuing a policy most of its members believe is right — and that might, indeed, be right. But there is not much more consensus, societal or scientific, about the costs and benefits of quantitative easing than there was about the personhood of the fetus.

You have to admire Bernanke for taking the heart. He frequently invokes the dual mandate Congress gave the Fed — to pursue maximum employment and stable prices over the long term.

He’s right, but the dual mandate is actually a source of his troubles. It gives the Fed broader responsibility — and, some would say, broader power -- than the current state of objective economic knowledge really supports.

Central banks in the rest of the world have only one mandate: to ensure price stability.

Would a single mandate would create an anti-inflationary bias at the Fed, disabling it in times of high unemployment like the current one? Actually, as Harvard economist Greg Mankiw has suggested, monetary policy today might well be just as expansionary under a price-stability mandate. That’s because the Fed would be required to fight both inflation and deflation — and deflationary pressures are strong at present.

But the political context would be much different. Under simpler rules, the central bank’s claims of legitimacy would be that much clearer, and its resistance to politicization that much stronger.

The central bank could focus on its job, with less worry about angry letters from Congress. And there would be one less scapegoat for politicians to blame when they fail to meet their own responsibilities.